Whatever counting method you are using and whatever reporting method you are using, it needs to be verifiable. I still can't believe we had ballots from 2016 that were destroyed after brin subpoenaed, without any consequence for those who had charge of their possession and safety.
This may not make sense intuitively, but counting paper scales quite well by being distributed to the polling locations and physically sorting the paper ballots. The Australian Electoral Commission documents the counting process quite thoroughly [0].
The only time counting paper takes a long time to get a win/lose result is when results are close enough that every vote needs to be counted. This is surprisingly rare in practice.
I mean, the 2000 US presidential election had a recount... that was cancelled. The Brexit referendum had a bunch of spending irregularities... but the result stands. The 2016 US presidential election had allegations of Russian interference... but the result stands.
It's pointless having an early electronic result and a late paper result if the early result always stands - the late paper result gives you nothing except a false sense of security.
In none of those cases was there proof that actual vote counts were altered.
There are still ongoing investigations into Russia's interference, but the side that the interference helped is the on that's currently in power, and there's enough ambiguity for them to avoid taking any direct action. If we'd had a paper ballots that proved that Russia hacked voting machines and actually changed 100k or so votes--I'm 100% confident we'd have had a completely different outcome.
In none of those cases was there proof
that actual vote counts were altered.
More broadly, I hoped to illustrate the fact winners oppose fishing expeditions to double-check election integrity.
I simply don't believe we have the option of getting the result wrong on the first announcement. It has to be right the first time. And because it has to be right first time, we should apply our most trusted counting method the first time; the addition of an early-but-untrustworthy count is a move in the wrong direction.
But you can. Many states already have automatic recount laws when vote totals are close. In many cases candidates can pay for recounts even if they aren't close.
Recounts are common in American politics, and sometimes they even change the result--Al Franken won in 2008 after a recount flipped the result.
The Florida recount would most certainly have been finished if any of the counties had found obvious cases of voting machine hacking. Every country completed at least 1 recount, and most completed manual recounts.